Find The Fake Coin
You have twelve coins. You know that one is fake. The only thing that distinguishes the fake from the real ones is that its weight is slightly different. You have a balance scale that only tells you whether or not both sides are even. Find a method to determine which coin is fake and whether it is heavier or lighter than a real one using the scale only three times.
Use only the twelve coins themselves and no others, no other weights, no cutting coins, no pencil marks on the scale... etc.